Find the matrix B of T with respect to the basis B = {~u1, ~u2}, where u1 is a unit vector that points along y = x toward increasing x and y and ~u2 is a unit vector that is perpendicular to ~u1 and 90 degrees counterclockwise from ~u1.

The matrix B is given as

Step-by-step explanation:

As the vectors are given by u1 and u2 where u1 is given as

As y=x thus

So the value of x and y is given as

Thus u_1 is given as

Now the vector u_2 is given as perpendicular to u_1 i.e.

So the B matrix is given as

So the matrix B is as above.

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